Domestic needing no Frenchman's encouragement (3)
I believe the answer is:
aid
'encouragement' is the definition.
(I've seen this before)
'domestic needing no frenchman's' is the wordplay.
'domestic' becomes 'maid' (maid is a kind of domestic).
'needing no' is a deletion indicator.
'frenchman' becomes 'M' (abbreviation for Monsieur - like 'Mr').
'maid' with 'm' taken away is 'AID'.
(Other definitions for aid that I've seen before include "charity" , "Care and help" , "Care, assistance" , "encouragement" , "Help. Assist" .)